To access your business pages news feed, look directly under your avatar and there is a box called View Pages Feed. Click on that and it will take you to that pages news feed. (As displayed below.)
It seems Facebook want you to sign up to business manager. It allows you to manage multiple pages with one account. Which you could and can still continue to do with out business manager. I’ve found it to be completely disastrous. Its clunky and not all that user friendly. Maybe it will get better…..
What they don’t tell you is once you have signed up, you are not able to take your business page back. (you can but you have to dig through endless forums to find out how) So beware. Read ALL the fine print before signing up.